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Mat. Tr., 2017, Volume 20, Number 2, Pages 52–79 (Mi mt323)  

This article is cited in 2 scientific papers (total in 2 papers)

Definable sets in generic structures and their cardinalities

I. Kiouvrekisa, P. Stefaneasa, S. V. Sudoplatovbcde

a National Technical University of Athens, Zografou, Greece
b Sobolev Institute of Mathematics, Novosibirsk, Russia
c Novosibirsk State Technical University, Novosibirsk, Russia
d Novosibirsk State University, Novosibirsk, Russia
e Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

Abstract: Analyzing diagrams forming generative classes, we describe definable sets and their links in generic structures as well as cardinality bounds for these definable sets, finite or infinite. Introducing basic characteristics for definable sets in generic structures, we compare them each others and with cardinalities of these sets.We introduce calculi for (type-)definable sets allowing to compare their cardinalities. In terms of these calculi, Trichotomy Theorem for possibilities comparing cardinalities of definable sets is proved. Using these calculi, we characterize the possibility to construct a generic structure of a given generative class.

Key words: definable set, generic structure, cardinality of set, generative class, calculus for definable sets.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00531_а
Ministry of Education and Science of the Russian Federation НШ-6848.2016.1
Ministry of Education and Science of the Republic of Kazakhstan 0830/ГФ4


DOI: https://doi.org/10.17377/mattrudy.2017.20.203

Full text: PDF file (330 kB)
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English version:
Siberian Advances in Mathematics, 2018, 28:1, 39–52

UDC: 510.67
Received: 01.02.2017

Citation: I. Kiouvrekis, P. Stefaneas, S. V. Sudoplatov, “Definable sets in generic structures and their cardinalities”, Mat. Tr., 20:2 (2017), 52–79; Siberian Adv. Math., 28:1 (2018), 39–52

Citation in format AMSBIB
\Bibitem{KioSteSud17}
\by I.~Kiouvrekis, P.~Stefaneas, S.~V.~Sudoplatov
\paper Definable sets in generic structures and their cardinalities
\jour Mat. Tr.
\yr 2017
\vol 20
\issue 2
\pages 52--79
\mathnet{http://mi.mathnet.ru/mt323}
\crossref{https://doi.org/10.17377/mattrudy.2017.20.203}
\elib{http://elibrary.ru/item.asp?id=30558044}
\transl
\jour Siberian Adv. Math.
\yr 2018
\vol 28
\issue 1
\pages 39--52
\crossref{https://doi.org/10.3103/S1055134418010030}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85043504428}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Sudoplatov, “Generations of generative classes”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 22 (2017), 106–117  mathnet  crossref
    2. S. V. Sudoplatov, “On generic structures preserving elementary equivalence and elementary embeddability”, Bull. Karaganda Univ-Math., 89:1 (2018), 70–76  isi
  • Математические труды Siberian Advances in Mathematics
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